In geometry, the distance set of a collection of points is the set of distances between distinct pairs of points.
Thus, it can be seen as the generalization of a difference set, the set of distances (and their negations) in collections of numbers.
Several problems and results in geometry concern distance sets, usually based on the principle that a large collection of points must have a large distance set (for varying definitions of "large"): Distance sets have also been used as a shape descriptor in computer vision.
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